Editor’s Introduction: We recall that Alfred Tarski arrived in the USA from Poland in September 1939. The present series of letters starts not quite three years after his arrival; this span of time allowed him to adapt himself tentatively to his situation, and to shift much of his attention from the problems of the Old World to those of his immediate surroundings.

Tarski's World 3.0 is an innovative and enjoyable way to introduce your students to the language of first-order logic. Using this program, students quickly master the meaning of the connectives and quantifiers, and soon become fluent in the symbolic language at the core of modern logic. Tarski's World allows the students to build three-dimensional worlds and describe them in first-order logic. They evaluate the sentences in the constructed worlds, and if their evaluation is incorrect, the program (...) provides them with a game that leads them to understand where they went wrong. The package is intended as a supplement to any standard logic text, or for use by anyone who wants to learn the language. The disk and manual contain over a hundred exercises from very basic to highly sophisticated. (shrink)

_Tarski’s World_ is an innovative and exciting method of introducing students to the language of first-order logic. Using the courseware package, students quickly master the meanings of connectives and qualifiers and soon become fluent in the symbolic language at the core of modern logic. The program allows students to build three-dimensional worlds and then describe them in first-order logic. The program, compatible with Macintosh and PC formats, also contains a unique and effective corrective tool in the form of a game, (...) which methodically leads students back through their errors if they wrongly evaluate the sentences in the constructed worlds. A brand new feature in this revised and expanded edition is student access to Grade Grinder, an innovative Internet-based grading service that provides accurate and timely feedback to students whenever they need it. Students can submit solutions for the program’s more than 100 exercises to the Grade Grinder for assessment, and the results are returned quickly to the students and optionally to the teacher as well. A web-based interface also allows instructors to manage assignments and grades for their classes. Intended as a supplement to a standard logic text, _Tarski’s World_ is an essential tool for helping students learn the language of logic. (shrink)

The Language of First-Order Logic is a complete introduction to first-order symbolic logic, consisting of a computer program and a text. The program, an aid to learning and using symbolic notation, allows one to construct symbolic sentences and possible worlds, and verify that a sentence is well formed. The truth or falsity of a sentence can be determined by playing a deductive game with the computer.

This text/courseware package presents a new approach to teaching first-order logic. Taking advantage of Tarski's World 4.0, the text skilfully balances the semantic conception of logic with methods of proof. The book contains eleven chapters, in four parts. Part I is about propositional logic, Part II about quantifier logic. Part III contains chapters on set theory and inductive definitions. Part IV contains advanced topics in logic, including topics of importance in applications of logic in computer science. The Language (...) of First-order Logic contains hundreds of problems and exercises for the user to work through. (shrink)

This book is intended, along with the computer program, to introduce the user to some of the most important concepts and tools of logic, including learning a new computer language.

In answering the question "what is a language?", the author goes beyond Tarski, Carnap and Quine--to whom he is at the same time greatly indebted--and suggests that there cannot be a logic without ontology, that language is conditioned by the world, and that full explication of the concept of language must include pragmatics, not merely syntactics and semantics. This important and fair-minded book presupposes a grasp of symbolic logic. --E. S.

Ranging from Joseph Bellamy to Hilary Putnam, and from early New England Divinity Schools to contemporary university philosophy departments, historian Bruce Kuklick recounts the story of the growth of philosophical thinking in the United States. Readers will explore the thought of early American philosphers such as Jonathan Edwards and John Witherspoon and will see how the political ideas of Benjamin Franklin, Thomas Paine and Thomas Jefferson influenced philosophy in colonial America. Kuklick discusses The Transcendental Club (members Henry David Thoreau, Ralph (...) Waldo Emerson) and describes the rise of pragmatism centered on Metaphysical Club of Cambridge (and members William James, Oliver Wendell Holmes, and Charles Peirce). He examines the profound impact Darwinism had on American philosophy and looks at Idealists such as the Kantian Josiah Royce and the Hegelian John Dewey. The book shows how, in the twentieth century, the Nazi conquest of Europe unleashed a flood of European intellectuals onto these shores, including such major thinkers as Theodore Adorno, Erich Fromm, Rudolph Carnap, and Alfred Tarski. Finally, Kuklick examines the contributions of such contemporary philosophers as Sidney Hook and Willard Quine and such books as John Rawl's A Theory of Justice and Herbert Marcuse's One Dimensional Man. Kuklick pulls no punches in portraying the state of American philosophy today and its contested role in the intellectual life of the nation and the world. The range of philosophical thought in our nation's history has been great, from Edwards's Religious Affections to Kuhn's The Structure of Scientific Revolutions, and Bruce Kuklick has captured it all in a book that blends intricate details with sweeping vision. (shrink)

Tarski has exerted enormous influence not only on the development of mathematical logic, but on twentieth-century philosophy and philosophical analysis. This influence has been twofold, with the two components pulling in a sense in opposite directions. A comparison with the influence of the Vienna Circle provides an instructive vantage point in viewing Tarski’s influence. On the one hand, Tarski has provided powerful tools for logical analysis in philosophy. His first and most important contribution was to show that — and how (...) — the crucial semantical concept of truth can be defined for various formal languages. They include the most central types of language used and studied by twentieth century logicians and philosophers. The subsequent work by Tarski and his school in creating contemporary model theory in its narrow sense as a branch of technical logic has likewise enriched tremendously the conceptual arsenal of philosophers. The extent and depth of Tarski’s influence is in fact easily underestimated. In comparison, Carnap’s well-known books in logical syntax and logical semantics did not in the same way contribute to the logical techniques that philosophers might find useful. A large part of Tarski’s influence lies in facilitating a switch of emphasis from purely syntactical to model-theoretical, semantical methods. It was Gödel’s and Tarski’s early work that forced logicians and philosophers for the first time to take seriously the distinction between semantical and syntactical concepts and methods. The general theoretical implications of the distinction were not realized at once. In the light of hindsight, it is for instance quite striking that Tarski still in his classical monograph repeatedly assimilates to each other the task of defining truth for some part of mathematics or logic and axiomatizing its truths in a sense that involves explicit syntactical rules of inference. It was nevertheless Tarski more than anyone else who began to develop and exploit systematically model-theoretical concepts in logical theory. In comparison, Gödel never developed systematically the model-theoretical aspects of logic. Others, for instance Quine, stubbornly remained within the syntactical tradition. Carnap, who did switch his attention from the syntactical to a semantical approach, was not powerful enough a logician to create a sufficiently rich store of model-theoretical techniques and ideas to be equally helpful in philosophical analysis. In contrast, several major developments in analytic philosophy have had their starting points in Tarski’s ideas. Well-known cases in point are Davidson’s truth-conditional semantics and the possible worlds semantics developed by Tarski’s favorite former student Richard Montague. (shrink)

Deflationsism about truth is a pot-pourri, variously claiming that truth is redundant, or is constituted by the totality of 'T-sentences', or is a purely logical device (required solely for disquotational purposes or for re-expressing finitarily infinite conjunctions and/or disjunctions). In 1980, Hartry Field proposed what might be called a 'deflationary theory of mathematics', in which it is alleged that all uses of mathematics within science are dispensable. Field's criterion for the dispensability of mathematics turns on a property of theories, called (...) conservativeness. I present some technical results, some of which may be found in Tarski (1936), concerning the logical properties of truth theories; in particular, concerning the conservativeness of adding a truth theory for an object level language to any theory expressed in it. It transpires that various deflationary truth theories behave somewhat differently from the standard Tarskian truth theory. These results suggest that Tarskian theories of truth are not redundant or dispensable. Finally, I hint at an analogy between the behaviour of mathematical theories and of standard (Tarskian) theories of truth with respect to their indispensability to, as Quine would put, our 'scientific world-view'. (shrink)

This paper is an edited form of a letter written by the two authors (in the name of Tarski) to Wolfram Schwabhäuser around 1978. It contains extended remarks about Tarski's system of foundations for Euclidean geometry, in particular its distinctive features, its historical evolution, the history of specific axioms, the questions of independence of axioms and primitive notions, and versions of the system suitable for the development of 1-dimensional geometry.

We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ?On the Concept of Following Logically?. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we (...) note more than 400 differences. Several dozen of these are substantive differences due to revisions by Tarski to the Polish version which he did not incorporate in the German version. With respect to these revisions the Polish version should be regarded as more authoritative than the German. Hence scholars limited to an English translation should use ours. (shrink)

In this article the author first described the developments which brought to focus the importance of consistency proofs for mathematics, and which led Hilbert to promote the science of metamathemat-ics. Further comments and remarks concern the (partly analogous) beginnings of the work on the decision problem, Gödel?s theorems and related matters, and general metamathematics. An appendix summarizes a text by the author on completeness and categoricity.

In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.

This book is well known for its proof that many mathematical systems - including lattice theory and closure algebras - are undecidable. It consists of three treatises from one of the greatest logicians of all time: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups.".

This article presents Tarski's Address at the Princeton Bicentennial Conference on Problems of Mathematics, together with a separate summary. Two accounts of the discussion which followed are also included. The central topic of the Address and of the discussion is decision problems. The introductory note gives information about the Conference, about the background of the subjects discussed in the Address, and about subsequent developments to these subjects.

We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ‘On the Concept of Following Logically’. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we (...) note more than 400 differences. Several dozen of these are substantive differences due to revisions by Tarski to the Polish version which he did not incorporate in the German version. With respect to these revisions the Polish version should be regarded as more authoritative than the German. Hence scholars limited to an English translation should use ours. (shrink)

Uncoupling proteins (UCPs) regulate mitochondrial function, and thus cellular metabolism. Angiotensin‐converting enzyme (ACE) is the central component of endocrine and local tissue renin–angiotensin systems (RAS), which also regulate diverse aspects of whole‐body metabolism and mitochondrial function (partly through altering mitochondrial UCP expression). We show that ACE expression also appears to be regulated by mitochondrial UCPs. In genetic analysis of two unrelated populations (healthy young UK men and Scandinavian diabetic patients) serum ACE (sACE) activity was significantly higher amongst UCP3‐55C (rather than (...) T) and UCP2 I (rather than D) allele carriers. RNA interference against UCP2 in human umbilical vein endothelial cells reduced UCP2 mRNA sixfold (P < 0·01) whilst increasing ACE expression within a physiological range (<1·8‐fold at 48 h; P < 0·01). Our findings suggest novel hypotheses. Firstly, cellular feedback regulation may occur between UCPs and ACE. Secondly, cellular UCP regulation of sACE suggests a novel means of crosstalk between (and mutual regulation of) cellular and endocrine metabolism. This might partly explain the reduced risk of developing diabetes and metabolic syndrome with RAS antagonists and offer insight into the origins of cardiovascular disease in which UCPs and ACE both play a role. (shrink)

Alfred Tarski’s theory of truth, to which we will also refer as the classical theory,1 has a conspicuous place in mathematics as well as in general philosophy. The place in philosophy appears the more prominent of the two, although it is still somewhat unsettled, and perhaps even controversial.

Cette Introduction à la logique constitue le cours de base des étudiants en sciences et en philosophie. La présentation de la logique formelle dans son contexte historique est accompagnée d'un exposé très clair des notions syntaxiques et sémantiques nécessaires au calcul des énoncés et au calcul des prédicats du premier ordre... Les méthodes formelles les plus classiques (tables de vérité, arbres de consistance, dérivations) sont explicitées au travers de nombreux exercices d'application accompagnés de leurs corrigés. La seconde partie de l'ouvrage (...) fournit au lecteur les contenus théoriques nécessaires à la compréhension des débats qui ont animés la philosophie de la logique et son dialogue avec les mathématiques depuis la fin du XIX, siècle. L'axiomatisation du calcul des énoncés (présentation de So), les notions de complétude sémantique et syntaxique comme le concept de décidabilité sont introduits. Un chapitre est consacré à l'axiomatisation du calcul des prédicats du premier ordre et permet de familiariser le lecteur à la métathéorie. La présentation des résultats fondateurs (théorème de consistance, théorème de Tarski, théorème de complétude) jette les bases de la théorie des modèles. Enfin, l'ouvrage s'achève par les fondations de la logique mathématique (système Se de la théorie des ensembles et système Sn de la théorie des nombres naturels) et par l'exposé des célèbres théorèmes de Gôdel... (shrink)

This article presents Tarski's Address at the Princeton Bicentennial Conference on Problems of Mathematics, together with a separate summary. Two accounts of the discussion which followed are also included. The central topic of the Address and of the discussion is decision problems. The introductory note gives information about the Conference, about the background of the subjects discussed in the Address, and about subsequent developments to these subjects.

Prologue, invitation to thinking about God In the Hebrew Bible? -- Part I, questions about God? -- Why does God in the Bible have a body? -- What do God's body parts in the Bible mean? -- Why is God angry in the Bible? -- Does God in the Bible have gender or sexuality? -- Part II, questions about God in the world? -- What can creation tell us about God? -- Who-or what-is the Satan? -- Why do people (...) suffer according to the Hebrew Bible? -- Epilogue, God in the Bible and beyond. (shrink)

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

Alfred Tarski was one of the greatest logicians of the twentieth century. His influence comes not merely through his own work but from the legion of students who pursued his projects, both in Poland and Berkeley. This chapter focuses on three key areas of Tarski's research, beginning with his groundbreaking studies of the concept of truth. Tarski's work led to the creation of the area of mathematical logic known as model theory and prefigured semantic approaches in the philosophy (...) of language and philosophical logic, such as Kripke's possible worlds semantics for modal logic. We also examine the paradoxical decomposition of the sphere known as the Banach–Tarski paradox. Finally we examine Tarski's work on decidable and undecidable theories, which he carried out in collaboration with students such as Mostowski, Presburger, Robinson and others. (shrink)

Tarski's correspondence theory of truth (which he spells out in his semantic conception of truth) is open to two interpretations. This ambiguity in the theory has led philosophers to find support in it for metaphysical realism. In fact, Tarski's theory turns out to support a form of ontological relativism. In different passages Tarski himself gives support to each of these interpretations. The first interpretation leads to ontological relativism, while the second sacrifices the connection between language and the (...) class='Hi'>world. I clarify the dilemma that I see in having to choose between these two interpretations, explain how these interpretations have their source in different problems which occupied Tarski, and consider a possible solution to the dilemma. Finally, finding good reasons to claim that Tarski's theory is indeed a correspondence theory of truth, I argue in favour of the first interpretation with its relativistic implications. (shrink)

This book examines Augustine's description of the actually existing world, especially that aspect most important for the human pursuit of happiness: the human being and God. It begins with an overview of the characteristics of the human individual and the context in which they must live out their lives, a context dominated by two seemingly contradictory realities: the existence of God and the existence of evil.

Articles on the relevance of Islam and a comparative look with European philosophy in the contemporary world.

In lieu of an abstract, here is a brief excerpt of the content:Consciousness and Machines:A Commentary Drawing on Japanese PhilosophyS. D. Noam Cook (bio)Viewed from within the great unity of consciousness, thinking is a wave on the surface of a great intuition.Kitarō NishidaIntroductionRecent developments in AI have made the long-standing debate about what computers can and can't do a major public concern. What we understand the properties of such machines to be, and consequently how we design [End Page 305] and (...) deploy them, will increasingly shape how we live and how we understand ourselves. Thus, there is an urgent need for better understanding of these issues.Susan Schneider, in her book Artificial You: AI and the Future of Your Mind, offers an exceptionally careful and insightful examination of key issues entailed in how we understand AI and ourselves. One of her central concerns is how we might test for machine consciousness. Given the variations in design and function among current and projected AIs, Schneider sees no likely one-size-fits-all test. So, she offers a battery of different tests that she believes together will make such testing more reliable. This seems a wise approach, and reflects the conceptual and pragmatic care Schneider takes throughout the book.Similarly, it seems to me that the question of machine consciousness should also include various understandings of consciousness itself. What consciousness is taken to be has varied widely both historically and culturally. No commonly accepted single understanding has emerged, and may never emerge. Just as having a battery of tests might help us better assess possible machine consciousness, having different understandings of consciousness might give us a better understanding of what we are testing for. The two should work in tandem, each gauging and shaping the other.Like the development of computers themselves, the predominant thinking about AI has been shaped, in part, by key presuppositions of a scientific worldview, with its origins in Western thought and culture. Among these presuppositions are materialism, reductionism, and a primary focus on objective behavior. These are reflected in the common concern with observable behavior of physical aspects of the brain in efforts to understand human consciousness, which in turn has become a familiar model for work on machine consciousness. All this is important and valuable work. But, in the spirit of Schneider's cautions, it should not be taken as one-size-fits-all. Accordingly, I offer one view of consciousness from a different perspective.In what follows, I sketch out an understanding of consciousness that draws on Japanese philosophy, particularly that of the highly influential early twentieth-century Japanese philosopher Kitarō Nishida (1870–1945). I then explore how the tests for machine consciousness that Schneider proposes might be viewed from that perspective.Consciousness: A Perspective from Japanese PhilosophyConsciousness was a central concern for Nishida, whose philosophy is deeply informed by Japanese culture and by Zen theory and practice. As one might expect from such a philosopher, Nishida's exploration of consciousness is not concerned with properties of the brain, but with what we might discern through disciplined reflection on the experience of our own consciousness. Ultimately, he views consciousness as an organic whole [End Page 306] of systemically organized interrelationships of activities and sensations within our subjective experience. This may be understood by first considering 'nothingness'.For Nishida, nothingness does not suggest an ultimate and absolute vacuity, as is often understandably assumed. In Nishida's sense, it is a singular "place" that mirrors the multifaceted world of our common experience. In understanding this, I am told by native Japanese speakers that the English word 'nothingness' has an advantage over the Japanese equivalent, 'mu', in that 'nothingness' can usefully be broken down as 'nothing-ness'. This suggests that nothingness is a state of consciousness where what we commonly experience as distinct (self, other, world, blue, ache, joy, etc.) is indistinct, a state of unified experience. This is consciousness without our finding or discriminating in it the myriad "things" of common experience, but rather a "pure experience" of a singular whole. Nishida introduces his concept of "pure experience" as follows:To experience means to know facts just as they are, to know in accordance with facts by completely relinquishing one... (shrink)

This book presents empirical studies of the rise, expansion, and influence of scientific discourse and organization throughout the world, over the past century. Using quantitative cross-national data, it shows the impact of this scientized world polity on national societies. It examines how this world scientific system and national reflections of it have influenced a wide variety of institutional spheres—the economy, political systems, human rights, environmentalism, and organizational reforms. The authors argue that the triumph of science across social (...) domains and around the world is due to its institutionalized cultural authority rather than to its instrumental utility for societies or for their dominant elites. Thus, following the Stanford approach to institutional theory in sociology, the book emphasizes the symbolic or religious role science plays in the modern world. (shrink)

This article defends the conclusion that the soccer World Cup in Qatar should not be boycotted by rich countries from the Global North. This conclusion is underpinned by considerations about the economic background conditions in guest workers’ home countries. Three arguments are considered for the view that the World Cup should be boycotted. It is argued that each of these arguments is unsound. Section 7 contains a discussion of an argument for a boycott that centers on the process (...) through which Qatar was awarded the World Cup. This argument is rejected. The article lists several ways in which guest workers in Qatar are wronged, but this fact about how guest workers are treated does not justify a boycott by rich countries from the Global North. (shrink)